arXiv:2405.07112 Abstract | arXiv Analytics

arXiv:2405.07112 [math.LO]Abstract References Reviews Resources

Definable compactness in o-minimal structures

Published 2024-05-12Version 1

We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of definable compactness in the literature, including those in terms of definable curves, definable types and definable downward directed families of closed sets.

Comments: This is a round-up of the topological content of arXiv:2111.03802

Categories: math.LO, math.GN

Subjects: 03C64, 54A05, 54D30

Keywords: definable compactness, o-minimal structures, topological spaces, answering questions, definitions

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